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Topic: An interesting property of ellipses
Replies: 1   Last Post: Jun 23, 1994 12:21 PM

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 John Conway Posts: 2,238 Registered: 12/3/04
Re: An interesting property of ellipses
Posted: Jun 23, 1994 12:21 PM

This is, or really I should say "was", a well-known property.
The locus of points from which an ellipse subtends a right angle
is usually called the "director circle", because the corresponding
locus for a parabola is its directrix.

Here's something you may like. Take a loop of string around your`
ellipse, into which you're going to put your pencil-point and
use it to draw a circumscribing curve, in a way that specializes
to the usual way of drawing an ellipse when the starting ellipse
degenerates to a line segment.

Then the curve you draw will be a confocal ellipse to the
original, and both the part of the string that touches the
inner ellipse, and the part that doesn't, remain of
constant length.

John Conway

Date Subject Author
6/22/94 Rouben Rostamian
6/23/94 John Conway